The Solution of Lagrange´s Equations by Analog Computation

A procedure for solving Lagrange´s equations of motion by analog computation is discussed. The problem of summing loop instabilities is minimized because the coefficient matrix of the acceleration terms in the generalized force equations is positive definite. No computer instabilities occur if external generalized forces do not contain acceleration-dependent terms (from rubbing friction). A two-dimensional example is analyzed and it is concluded that the existence of such terms will rarely cause computer instability for realistic physical systems. This paper also includes special techniques for systems which are conservative, contain cyclic co-ordinates, or are subject to nonholonomic or holonomic constraint equations.